Why do trains stay on the track as they go around a curve?

The other night, Joshua Foer posed this question was posed to a table full of science journalists. Most of us started talking about friction, and/or possibly something to do with the little flanges on either side of a train wheel.

We were all wrong.

This is a Richard Feynman video, yes, but it's more about mechanics than physics. Turns out, you can learn a lot about how trains stay on the track by looking under your own car.


  1. Eli. if you think Arthur`s postlng is neat… on saturday I bought themselves a opel since getting a check for $8225 this-last/5 weeks and-even more than, ten thousand this past munth. no-doubt about it, this really is my favourite-job I have ever had. I began this seven months/ago and pretty much straight away started making a cool over $80, per-hour. I use the details on this web-site, fab22.comCHECK IT OUT

  2. It’s because they have training wheels. If they didn’t have training wheels, they couldn’t go around curves.

  3. Ain’t that neat? There are other technologies that assist in getting around those corners, including tilting systems and articulated bogies. Isn’t that last a great phrase? Another neat phrase: The back-and-forth phenomenon Feynman alludes to when talking about the natural error-correcting tendency of coned wheels on adhesion railway systems is called “hunting oscillation.” Train terminology is great, as any gandy dancer knows.

    I’ll take this opportunity to recommend China Mieville’s recent one-off novel, “Railsea.”

    1. my classmate’s sister makes $76/hour on the computer. She has been for laid off for 9 months but last month her paycheck was $16155 just working on the computer for a few hours. Read more on  Jive8.c­om

  4. It’s very very bad to use “and/or” construct in any text but especially wrong in scientific context. Logic OR operation already includes AND operation in it. There is an aditional logic operation called Exclusive OR (XOR for short) which does not include AND operation. Logic operation of XOR translates to spoken everyday english into “either… or…” construction, which si used if you want to express the two mutually exclusive choices. Writing XOR/AND would make sense but writing AND/OR just shows that the writer doesn’t have any grasp of elementary logic. This is made even worse by the fact that this ugly construction is usually written in texts when people try to pe accurate and precis.

    1. You would be correct, if the writing in question were a proof in symbolic logic. Ordinary usage does not agree.

      1.  Exactly so.  Common usage of “or” differs from logic OR, in that people will generally take it to mean mutually exclusive choices: “You can do this, or you can do that”.  Writing “and/or” where the options aren’t mutually exclusive is clearer to the general readership, which is where this piece is aimed.

        1. I think it would be a great improvement to the English language if ‘and’ and ‘or’ took on the common symbolic logic meanings, and ‘xor’ were introduced into common usage.

          1. “I think it would be a great improvement to the English language”
            The language changes according to usage, of course, so no need to sit on your hands — simply start using “xor” yourself. Perhaps it will catch on.

          1. I actually was totally confused by this saying my entire childhood until I found out the modern American usage actually reversed from the original English one, “He wants to eat his cake and still have it!”  The original English usage makes immediate common sense compared to our popular American vernacular, “He wants to have his cake and eat it!”, which to me as a kid was precisely the point of having a cake in the first place!

        2. It depends on context. usually inclusive or, sometimes exclusive or, and/or where it’s inclusive but the context might allow an exclusive interpretation.

      1. Those errors look planted; P is nowhere near B. Maybe trying to put a few errors in there to preempt Muphry’s Law?

    2. I personally think it’s very bad, or at least ridiculously impolite, to play the self-appointed language expert based on one’s half-baked language usage preferences. If you can’t figure the meaning of “and/or” on your own, you could try reading Maggie’s text for comprehension. It’s quite obvious: some started talking about friction, some about little flanges, and some about both. That’s what “and/or” commonly means in informal, everyday English. HTH.


      Writing XOR/AND would make sense but writing AND/OR just shows that the writer doesn’t have any grasp of elementary logic.

      Actually, what it shows is that the author is not an obnoxious pedant.  Everyone — including obnoxious pedants — understands exactly what the author means and no one — even obnoxious pedants — really thinks that this construction indicates anything about the author’s grasp of symbolic logic. 

      In common usage, “or” is often used to mean exclusive or because most people employing common usage are unaware of the XOR construction.  Furthermore, XOR is not really part of standard spoken English (unless you’re a huge nerd) and is almost as obnoxious to pronounce as “Ubuntu”.  Thus “and/or” in common usage serves the purpose of disambiguating the term “or” which, despite its use in symbolic logic, is indeed ambiguous in common usage.

      1. I agree with most of your post but there’s nothing wrong with saying Ubuntu, it’s just a Bantu  word that is an African philosophy of human unity

        1. I (personally) find it difficult and annoying to pronounce.  The etymology of the word is completely irrelevant to this fact. That’s not my only reason for switching to mint but it’s actually one of the major ones.

          There’s nothing wrong with saying it if you like saying it.  I don’t. For similar reasons I hate trying to pronounce “Au Bon Pain” correctly and just call it “ABP”.

    4. i guess you could say StaneStane really
      derailed this thread.

    1. And what’s just as important in a way, a not-explainer.  I went on from that video to the one where he tells the interviewer that he won’t explain [frickin’] magnets, because they’re just a pretty basic and very common force, and [unless you’re a physicist] what else is there to explain? 

      But I really can’t do a good job, any job, of explaining magnetic force in terms of something else that you’re more familiar with, because I don’t understand them in terms of anything else that you’re more familiar with.

        1. Well the ICP were explaining them in terms of something they were more familiar with, that something being magic.

          1. “Well the ICP were explaining them in terms of something they were more familiar with, that something being magic.”
            That brings up a great point: what is means TO be familiar with, or knowledgeable about, something. A collection of ideas that isn’t systematic and coherent — such as the impressionistic and largely fictional collection of ideas known as “magic” — ISN’T something we can be knowledgeable ABOUT. (I’m here talking of supernatural magic, not stage magic.)

          2. I’ve come to see that Harry Potter-style “supernatural magic” has no resemblance whatsoever to what practitioners of ritual magic and the occult consider to be magic — which is mostly mind-hacking.  But since stage magicians are essentially just mind-hacking their audience I’ve come to see stage magic as a form of real magic (a little bit tacky and mercantile but magic nonetheless).

            Another way to think about it: the “placebo effect” is science’s way of admitting that ritual magic works.  Four pills works better than two, and the pills work better if the doctor wears a lab coat and says some “magic words” (sciencey-sounding terminology) when he or she gives them to you. 

            You can understand magic just fine, you just need to keep an open mind and not get side-tracked by fictional misrepresentations of it.

  5. ” Turns out, you can learn a lot about how trains stay on the track by looking under your own car.”

    Actually, after listening to that explanation, I would venture to say that you can actually learn nothing at all about how a train stays on the track by looking under your car.

    But thanks for a fascinating video clip

    1. “I would venture to say that you can actually learn nothing at all about how a train stays on the track by looking under your car.”
      No? I thought it was pretty useful!

      Look under your car.
      What do you observe about the axle?
      It’s cut in half! How come?

      Noticing the differential gives you a reason to ask questions about its function, which lead to less apparent aspects of mechanics.

      1. Zachary_Bos: “What do you observe about the axle?It’s cut in half!”

        If you can actually “observe” this, you probably shouldn’t spend much time thinking about trains.

      2.  I have looked under my car, I know what a differential is, how it works, and what problem it is there to solve. And that does exactly nothing towards furthering my understanding of how a train solves that same problem, because a train does it in a way that is completely and utterly different.  My first thought upon seeing that line was “Wait a minute – trains use
        differential gears? Huh, how about that” and I
        suspect I’m not alone.

        This is akin to saying “Turns out, you can learn a lot about how solar panels generrate electricity by looking at your alternator”

    1.  Right. How is this not physics? If you’re trying to understand the mechanisms behind the behavior of a physical system (that works in terms of forces and so on), it’s physics. Sure, it doesn’t deal with quantum or relativistic phenomena, and the trends and mechanisms are described qualitatively instead of numerically, but I think it still counts as physics. Saying that ‘this is not physics” reminds me of when kids are tricked into learning something, and you tell them that it’s science or math or history or whatever, and they reply “No, this isn’t [science or math or history or whatever], this is FUN!”, because they define those terms narrowly based on how those topics are taught in school (rather than defining them based on what topics they tackle, how they tackle those topics, and why).

  6.  http://en.wikipedia.org/wiki/Cant_%28road/rail%29

    Superelevation. The train stays on the track in the curve because superelevation….

    1.  Yeah, that’s what I thought.  I’m sure the tapered wheel bit is true, but I would certainly expect that they(tm) thought of tilting the tracks before they thought of tapering the wheels.  And since railroad tracks are in fact tilted… er, superelevated… around corners, I’m sure that’s an important part of the answer.

      1. I think the thing is, it doesn’t matter how fast the train is moving.  If you had flat wheels and a straight track the train would eventually just be riding on the flanges, with accompanying squealing and wear.  The taper keeps the train centered on the tracks.

        And actually thinking about it, if the two wheels could spin independently, the train would slide to one side and you’d get the squealing from running on the flanges.  So the solid axle is critical to make the system work.

    2. according to the 1925 article linked to by that wikipedia page, canting doesn’t keep the train on the tracks; it just saves on wear by keeping the wheel more centered. only about half the railroads at the time bothered.

    3. The problem is, the article title doesn’t actually describe the video. It’s not about why trains stay on the track on a curve, but all the time. If you imagined a train with no wheel flanges just sitting precariously atop those narrow rails, you’d expect it to slip off the track even on a straightaway. But you’d be wrong, and Feynman explains why.

      1. “It’s not about why trains stay on the track *on a curve*, but *all the time *. ”
        Au contraire! The beveled wheels eliminate the need for a differential: by riding onto a cone section with a larger radius, the outer wheel (rotating at the same speed because of the fixed axle) covers more ground, so to speak.

        1. There is a “curved” train station near where I live. The effect described above doesn’t work for slow trains, since there isn’t enough centrifugal force. However, the trains do stay on track, but with a lot of very loud squeaking. 

          The shape of the wheels does keep the train on track (gravity keeps it centered), but the differential part is only a bonus. 

  7. I knew the tapered wheels on a train were used to function in the same way as a differential, but I’d never associated that with the ability for the train to stay on a straight section of tracks.

    It would be totally awesome to read about how that solution came into being and how badly trains performed before it was developed. Or was the technique adapted from some earlier system?

    1. “It would be totally awesome to read about how that solution came into being and how badly trains performed before it was developed.”
      A term to search for, actually, is “hunting oscillation.” It was a problem, and it remains a problem (think of speed limitations on passenger rail service in the Northeast Corridor…)

    2. Wooden two-rail cart-tracks were widely used in some parts of England. Obviously it wasn’t a disaster if a few carts went off the rails, but I imagine it was enough of a nuisance that they may have developed ways to keep them on the rails. I can’t imagine someone trying to put a steam train on the rails unless they were confident it would stay on the rails.

    3. The interesting part for me here is that you would’ve required very precise engineering to enable the tapered wheels, otherwise you would deal with a ton of oscillation. 

      Flanges would’ve been a simpler solution and tapering wouldn’t have arisen out of trying to keep trains on tracks, at least not until precision machining. For example, mining cart wheels don’t seem tapered.

      Early trains likely used the same solution as early vehicles: a single drive wheel with all wheels free.

    1. “Could it be for the same reason a belt stays on a convex roller?” Which is what — fear of reprisal for poor performance?

  8. I recommend to everyone to visit the National Railway Museum in York (UK). As well as being free at the point of entry and having a huge and fascinating collection of locomotives and other train goodness (including the Mallard), it also has one of those rooms full of things for kids to interact with (that as an adult I find even more fascinating) which includes a demo of this. Lots of wheel pairs of different shapes and a bit of curved track to roll them on.

    1. I remember going there as a teenager – I’d forgotten about the bevelled wheel pairs, but I remember finding them really interesting.

  9. Whew! I answered a question on Shorpy the other day about why the locomotive wheels were tapered, and gave the same explanation that Feynman gave. It’s pretty obvious once you think about it. But it must have been a leap of insight to the person who first came up with the idea a zillion years ago.

    You’ll also notice on any flat belt system, such as a belt sander, that the moving belt is kept centered by having the center of its pulley larger in diameter than the ends.

  10. The train goes stays on the track as it goes around a curve.  You can’t explain that.

    1.  his accent in the posted video is hugely decimated after living on the West Coast for decades.  Check out when he was young:

  11. In the beginning of the railroads, there were lots of situations where the last car jumped off the rails in curves, but the solution was pretty simple: they just took away the last car.

    1.  Wouldn’t the fact that the last car jumped off the rails take care of taking away the last car?

      …wait… you can’t take away the “last” car… that’s recursive…

  12. Jeepers, and all this time, I thought they stayed on the track because trains are freakin’ heavy…

    1.  yeah, my initial guess was “gravity.”  but I guess when they get going fast enough, the “tendency to stay in motion” outweighs gravity at some point.

  13. Yes, it sure sounds logical.  But take away the flanges, and it will derail every time.  I suspect the flanges get a bit more credit than he thinks….

  14. I actually disagree with this. The Flanges aren’t simple safety mechanisms… You hear them grinding on the side of the tracks too frequently to be discounted as playing a significant part in keeping the train on the tracks.

  15. I first read this paired with another riddle from Feynman: why do mirrors only reverse images left-to-right, and not up-and-down? What’s so special about the horizontal axis?

    If my computer desk hadn’t been shiny, it would have taken me ages to figure out.

Comments are closed.